Bernstein approximations of Dirichlet problems for elliptic operators on the plane
Texas State University-San Marcos, Department of Mathematics
We study the finitely dimensional approximations of the elliptic problem (Lu)(x, y) + φ(λ, (x, y), u(x, y)) = 0 for (x, y) ∈ Ω u(x, y) = 0 for (x, y) ∈ ∂Ω, defined for a smooth bounded domain Ω on a plane. The approximations are derived from Bernstein polynomials on a triangle or on a rectangle containing Ω. We deal with approximations of global bifurcation branches of nontrivial solutions as well as certain existence facts.
Dirichlet problems, Bernstein polynomials, Global bifurcation
Gulgowski, J. (2007). Bernstein approximations of Dirichlet problems for elliptic operators on the plane. <i>Electronic Journal of Differential Equations, 2007</i>(86), pp. 1-14.